Mechanisms for Catalytic CO Oxidation on SiAun (n = 1–5) Cluster

Significant progress has been made in understanding the reactivity and catalytic activity of gas-phase and loaded gold clusters for CO oxidation. However, little research has focused on mixed silicon/gold clusters (SiAun) for CO oxidation. In the present work, we performed density function theory (DFT) calculations for a SiAun (n = 1–5) cluster at the CAM-B3LYP/aug-cc-pVDZ-PP level and investigated the effects on the reactivity and catalytic activity of the SiAun cluster for CO oxidation. The calculated results show that the effect is very low for the activation barriers for the formation of OOCO intermediates on SiAu clusters, SiAu3 clusters, and SiAu5 clusters in the catalytic oxidation of CO and the activation energy barriers for the formation of OCO intermediates on OSiAu3, OSiAu4, and OSiAu5. Our calculations show that, compared with the conventional small Au cluster, the incorporation of Si enhances the catalytic performance towards CO oxidation.


Introduction
Metal clusters have long been extensively studied due to their unique optical, electronic, and mechanical properties, as well as their wide range of applications in catalysts [1][2][3][4]. Among the various types of metal clusters, Au clusters have attracted much attention as size-tunable prototypes, because they have been shown to have significant catalytic activity [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Chen et al. [20] showed that Au loading and the Au particle size have significant effects on the generation of methanol and CO; with an increase in the Au loading/Au particle size, the generation activity (Au-mass-normalized reaction rate, TOF) for methanol and CO decreases, while the selectivity for methanol generation increases. The decrease in activity is mainly due to the decrease in the dispersion of Au particles, which is the particle size effect. A comprehensive time-resolved Operando-DRIFTS study of the evolution of various surface species during CO oxidation under high-temperature oxidation conditions for Au/CeO 2 catalysts (Au particle size range: 1.7 ± 0.6~3.7 ± 0.9 nm) was carried out by Huang et al. [13]. A new perspective on size-effect-supported Au catalysts for CO oxidation is presented; different size-dependent reaction pathways contribute to catalytic activity. Gold clusters are easier to aggregate than various other particles because of their higher surface energy [21][22][23]. Experimental and theoretical studies have been carried out to understand the high catalytic activity of gold clusters and particles. Gold clusters exhibit an excellent ability to catalyze a variety of industrially and environmentally important chemical reactions, such as propylene oxidation [24][25][26], the hydrodeoxygenation of guaiacol [27], the catalytic reduction of 4-nitrophenol [28] and graphene oxide [29], and the 1,2-aminoarylation of alkenes with external amines [30]. Luo et al. [4] investigated the conversion of glycerol-free oxidants to the corresponding aldehydes on simply generated small gold clusters using a simple LAL method. The activation mechanisms for C-O, C-H, and O-H bonds were thoroughly investigated to verify the feasibility of an oxidant-free dehydrogenation strategy catalyzed by small gold clusters produced by aqueous-phase synthesis. Azita et al. [9] investigated the methanol generation reaction over two Au/CeO 2 Molecules 2023, 28, 1917 2 of 15 catalysts with different gold loading by kinetic and in situ spectroscopy (DRIFTS) measurements, using isotopic labeling techniques, to further elucidate the role of the carrier in the methanol generation reaction for CO 2 and H 2 over oxidatively loaded gold catalysts. Gold catalysts have emerged as inimitable π-Lewis acids for selective functionalizations of C-C multiple bonds [31]. Patil et al. [32] developed the first process for the gold-catalyzed 1,2diarylation of alkenes by designing a mechanistic paradigm that integrates ligand-enabled Au(I)/Au(III) catalysis with the intrinsic π-activation ability of gold complexes.
One of the reactions that has received the most attention in the field of heterogeneous catalysis is CO oxidation [33][34][35]. Both experimental and theoretical studies have investigated the catalysis of CO oxidation by cluster [36][37][38][39][40][41][42][43][44][45][46][47]. Payam et al. [36] found that the catalytic activity of Pd/TiO 2 /Ti metal-supported catalysts was improved by the introduction of Zn, especially at Pd:Zn = 2:1, which reduced the binding energy of CO on the surface and improved the dissociative adsorption of oxygen, which facilitated the oxidation of CO. The work of Cai et al. [37] used density flooding theory (DFT) calculations for CO-catalytic oxidation over a single-atom catalyst, Ti/V 2 CO 2 , to investigate the effect of H 2 O on COcatalytic oxidation performance and its mechanism, and the study revealed the regulatory mechanism of water molecules in the CO oxidation process over Ti/V 2 CO 2 . Chen et al. [38] showed that the presence of oxygen vacancies and active Cu could enhance the oxidation activity of CO on TiO 2 substrates, as well as a large number of oxygen vacancies, although promoting the generation of O ads also weakened the redox performance of the catalyst. Compared with the effect of oxygen vacancies on the catalytic oxidation performance of CO, Cu + has a stronger effect on the catalytic oxidation performance of CO. Yoshida et al. [39] showed that Au δ+ is an adsorption site for CO and that adsorbed water promoted CO oxidation by Au/POM catalysts. This is the first report of CO oxidation using Au/POM catalysts, and their use has the potential to be extended to various gas-phase reactions. Soni et al. [41] used a novel synthesis method for the preparation of Au@Ti-SiO 2 with an optimum gold NP size (3-5 nm) using the sol-gel method in one step; for Si/Ti ratios of 10 (ATS 10) and 50 (ATS 50), the activity dramatically increased after treatment in a nitrogen flow, with almost 100% conversion of CO at room temperature.
It is generally believed that Au clusters are the most active catalysts for CO oxidation [48,49]. With regards to CO oxidation in gold clusters, over the past few years, experimental [50] and theoretical [51] studies have shown that small gas-phase gold oxide cluster cations with one atom-bound oxygen atom (Au n O + , n = 1-3) are active and selective for the oxidation of CO to CO 2 , which can occur via both Eley-Rideal-and Langmuir-Hinshelwood-like mechanisms. Recently, Zeng and coworkers [52] used ab initio calculations to show that catalytic activity decreases with increasing adsorption amounts. In particular, it has been shown that smaller gold clusters exhibit higher reactivity to CO and O 2 [16,53]. In addition, the electronic environment in clusters can be tuned by combining foreign atoms [16,[53][54][55]. For example, Au-Ag clusters catalyze CO oxidation [56]. GJena et al. revealed the effects of binding single hydrogen atoms in gold clusters through theoretical calculations [57]; this showed that introducing impurities such as H atoms in gold clusters can be highly efficient and cost-effective compared with using pristine gold clusters for CO oxidation. For example, He et al. reported a highly selective Au/ZnO composite catalyst for the one-step oxidative coupling of CO with secondary amines, producing oxamides [58]. SiAu silicides were experimentally reported in early 1964 by Barrow et al. [59]. Pal et al. [60] systematically studied the structural evolution of SiAu n clusters and found that gold clusters have evidently different structures after silicon incorporation. In a previous study, Kiran et al. reported a series of Si-Au clusters [61,62]. Wang et al. showed that they found relatively large embedding energies and small HOMO-LUMO gaps for AuSi 12 structures, with enhanced chemical activity and good electron transfer properties being revealed [63]. Although the reaction activity of gold clusters strongly depends on their shape and electron distribution [64,65], little is known about the catalytic activity of SiAu n clusters for CO oxidation.
In this work, we explored the effects of the incorporation of Si on the catalytic activity of gold clusters. In order to better study the effects of gold clusters and the incorporation of Si on the catalytic activity of gold clusters, we studied the structure of a SiAu n (n = 1-5) cluster and the catalytic oxidation of two CO molecules using it. The activation barriers for these reactions were calculated and compared with those when using the original gold cluster.

Results and Discussion
The most stable structures of the gold cluster, Au n (n = 1-6), as well as the SiAu n (n = 1-5) cluster, are provided in Figures S1 and S2 (the figures with the prefix S are provided in the Supplementary Materials). The optimized geometries of the Au n (n = 1-6) and SiAu n (n = 1-5) clusters are consistent with the structures recently reported in the literature [66,67]. The interaction between gold and O 2 is much weaker than that between gold and CO [15,68]. We first consider the structure and adsorption of carbon monoxide on pristine and SiAu n (n = 1-5) clusters, as shown in Figure 1 and Figure S3.

The Oxidation of CO on SiAun (n = 1-5) Cluster
We consider the catalytic oxidation of CO molecules by SiAun cluster. Landman and co-workers revealed a Langmuir−Hinshelwood (L-H) type of reaction mechanism for CO oxidation on Au8 supported by defect-free and defect-rich magnesia thin films using TPR experiments and ab initio calculations [75]. It is worth noting that transition-metal-bonded gold clusters can act as very efficient catalysts for CO oxidation with quite low activation barriers of 4.61-6.92 kcal/mol [76].
The CO oxidation reaction proceeds via the Langmuir-Hinshelwood (L-H) mechanism or the Eley-Rideal (E-R) mechanism [77], where CO is chemisorbed onto the catalyst and O2 is chemisorbed (L-H) or physically adsorbed (E-R) on the catalyst. The first step is the O2 reaction with the first CO molecule forming CO2 and an adsorbed O atom in Equa-tion1. The second step is the adsorbed atom O reaction with the second CO molecule to form CO2, and this leads to the recovery of the catalyst in Equation (2). CO + O2 + SiAun = CO2 + OSiAun (1) OSiAun + CO = CO2 + SiAun (2)  CO adsorption on the gold cluster was repeated to check the reliability of the chosen methods. The favorable adsorption geometries of CO on the Au n (n = 1-6) cluster found herein are consistent with the previous results reported in the literature [14,[69][70][71]. CO prefers to adsorb at the vertex position of small Au clusters, where top coordination was also found to be preferred. Phala showed that for clusters larger than Au 6 , the top configuration still dominates [72]. Figure S3 shows the adsorption energy of −9.22 kcal/mol for CO on Au, which is in agreement with the result of −9.92 kcal/mol calculated by Tielens et al. [73]. The adsorption energy of CO on Au 2 is computed to be around −29.75 kcal/mol, which is in agreement with the result of −29.06 kcal/mol calculated by Schwerdtfeger et al. [69]. The adsorption energies of CO on the Au n (n = 3-6) cluster are estimated to be −33.44 kcal/mol, −8.30 kcal/mol, −20.52 kcal/mol, and −16.83 kcal/mol, respectively, which are in agreement with the calculations of Wu et al. [14] and Xu et al. [74]. For the Au n (n = 1-3) cluster, the CO adsorption energy increases with the increasing cluster size, and for larger clusters of Au n (n = 4-6), the CO adsorption energy decreases with the increasing cluster size. This has also been reported in previous investigations [14,70]. This shows that the chosen method is reliable for investigating CO oxidation.
The sites at which CO binds to the SiAu n (n = 1-5) cluster exhibit similar features for the Au n (n = 1-6) cluster, as listed in Figure 1. The adsorption energy is computed to be −5.07 kcal/mol when CO is adsorbed on Au atoms for SiAu, while it is estimated to be −22.37 kcal/mol for the CO adsorption site on the Si atom of SiAu. When CO is adsorbed on the gold atom of the SiAu 2 cluster, the adsorption energy is −11.76 kcal/mol, while when it is adsorbed on the Si atom of the SiAu 2 cluster, the adsorption energy is −13.84 kcal/mol (see Figure S4 for the structure diagram of CO adsorbed on Au atoms). Therefore, for the small SiAu n (n = 1-2) cluster, the optimal structure is CO adsorption on the Si site. For the SiAu n (n = 3-5) cluster, CO binding to the apex of the SiAu n (n = 3-5) cluster is the most stable structure. The adsorption energies of CO on the SiAu n (n = 3-5) cluster are −18.45 kcal/mol, −20.52 kcal/mol, and −17.30 kcal/mol, respectively. It is noted that the adsorption energies of CO on the SiAu n (n = 1-3) cluster are larger than those of pure golds.

The Oxidation of CO on SiAu n (n = 1-5) Cluster
We consider the catalytic oxidation of CO molecules by SiAu n cluster. Landman and co-workers revealed a Langmuir−Hinshelwood (L-H) type of reaction mechanism for CO oxidation on Au 8 supported by defect-free and defect-rich magnesia thin films using TPR experiments and ab initio calculations [75]. It is worth noting that transition-metal-bonded gold clusters can act as very efficient catalysts for CO oxidation with quite low activation barriers of 4.61-6.92 kcal/mol [76].
The CO oxidation reaction proceeds via the Langmuir-Hinshelwood (L-H) mechanism or the Eley-Rideal (E-R) mechanism [77], where CO is chemisorbed onto the catalyst and O 2 is chemisorbed (L-H) or physically adsorbed (E-R) on the catalyst. The first step is the O 2 reaction with the first CO molecule forming CO 2 and an adsorbed O atom in Equation (1). The second step is the adsorbed atom O reaction with the second CO molecule to form CO 2 , and this leads to the recovery of the catalyst in Equation (2).
OSiAu n + CO = CO 2 + SiAu n (2) With regard to even-numbered gold clusters, they are highly active in CO oxidation compared with odd-numbered gold clusters [52,70,78]. In order to compare the effects on CO oxidation with the incorporation of Si on gold clusters, we firstly recalculated the oxidation of CO with a pristine small Au n (n = 1-2) cluster (see Figures S5 and S6). The reaction pathway for CO oxidation on Au 2 is shown in Figure S6. The formation of an OCOO intermediate is not energetically favorable, as the reaction energy is calculated to be 23.75 kcal/mol, as shown in Figure S6.
We then considered the oxidation of CO catalyzed by a SiAu cluster, as shown in Figure 2. We note that the rate-determining step for the formation of the OCOO intermediate is from A-IM1 to A-TS1, with an activation barrier of only 6.46 kcal/mol, as depicted in Figure 2a. Moreover, the process is exothermic, with a value of −60.42 kcal/mol. Therefore, the SiAu dimer can remarkably promote the formation of the OCOO intermediate. The formed OCOO intermediate is further decomposed into CO 2 and OSiAu, with a lower activation barrier of 13.15 kcal/mol from A-IM2 to A-TS2, as listed in Figure 2a. However, from Figure 2b, we find that the activation barrier leading to the formation of OCO intermediate formation from A-IM4 to A-TS3 is very high, with a value of 25.13 kcal/mol on the OSiAu. Moreover, in Figure S6b, the activation barrier for the formation of OCO from G-IM5 to G-TS4 is only 3.23 kcal/mol on the unbonded pristine Au 2 -O cluster. It is noteworthy that the bonded SiAu cluster shows a remarkable improvement in its catalytic effects for the first CO oxidation reaction and the formation of OSiAu compared with the Au 2 dimer, but the catalytic ability for the second CO is weakened, and the recovery of SiAu is not quite feasible. Thus, the difference in electron transfer from the supports to the Au particles can partially explain the above phenomenon [11]. activation barrier of 13.15 kcal/mol from A-IM2 to A-TS2, as listed in Figure 2a. However, from Figure 2b, we find that the activation barrier leading to the formation of OCO intermediate formation from A-IM4 to A-TS3 is very high, with a value of 25.13 kcal/mol on the OSiAu. Moreover, in Figure S6b, the activation barrier for the formation of OCO from G-IM5 to G-TS4 is only 3.23 kcal/mol on the unbonded pristine Au2-O cluster. It is noteworthy that the bonded SiAu cluster shows a remarkable improvement in its catalytic effects for the first CO oxidation reaction and the formation of OSiAu compared with the Au2 dimer, but the catalytic ability for the second CO is weakened, and the recovery of SiAu is not quite feasible. Thus, the difference in electron transfer from the supports to the Au particles can partially explain the above phenomenon [11]. With regard to the Au3 cluster, it was found that the rate-determining step of H-IM1 to H-TS1 for the oxidation of CO on Au3 to form the OOCO intermediate requires an activation energy barrier of 35.98 kcal/mol, as shown in Figure S7a. In contrast, the activation With regard to the Au 3 cluster, it was found that the rate-determining step of H-IM1 to H-TS1 for the oxidation of CO on Au 3 to form the OOCO intermediate requires an activation energy barrier of 35.98 kcal/mol, as shown in Figure S7a. In contrast, the activation barrier is only 1.15 kcal/mol for the second CO oxidation process on the Au 3 O cluster, from H-IM5 to H-TS4, to generate OCO intermediates, as listed in Figure S7b. This is in agreement with an earlier investigation [79]. For the oxidation of CO on the SiAu 2 cluster, the activation energy barrier for the first step from B-IM1 to B-TS1 is 26.29 kcal/mol, leading to the formation of an OOCO intermediate during CO oxidation in Figure 3a. Thus, SiAu 2 reduces the activation energy barrier for CO oxidation compared with the unbonded pristine Au 3 cluster. As shown in Figure 3a, the formed OCOO intermediate is decomposed into CO 2 and OSiAu 2 , with a high activation barrier of 23.76 kcal/mol from B-IM2 to B-TS2. However, from Figure 3b, we find a very high activation barrier for the formation of an OCO intermediate, with a value of 9.91 kcal/mol from B-IM5 to B-TS3 in the case of the Si-bonded OSiAu 2 cluster. However, on the unbonded pristine Au 3 -O cluster in Figure S7b, the activation barrier for the formation of OCO is only 1.15 kcal/mol. The catalytic ability of the SiAu 2 cluster is very low for CO oxidation. The slight difference may be attributed to the size effect of gold clusters [80].
barrier is only 1.15 kcal/mol for the second CO oxidation process on the Au3O cluster, from H-IM5 to H-TS4, to generate OCO intermediates, as listed in Figure S7b. This is in agreement with an earlier investigation [79]. For the oxidation of CO on the SiAu2 cluster, the activation energy barrier for the first step from B-IM1 to B-TS1 is 26.29 kcal/mol, leading to the formation of an OOCO intermediate during CO oxidation in Figure 3a. Thus, SiAu2 reduces the activation energy barrier for CO oxidation compared with the unbonded pristine Au3 cluster. As shown in Figure 3a, the formed OCOO intermediate is decomposed into CO2 and OSiAu2, with a high activation barrier of 23.76 kcal/mol from B-IM2 to B-TS2. However, from Figure 3b, we find a very high activation barrier for the formation of an OCO intermediate, with a value of 9.91 kcal/mol from B-IM5 to B-TS3 in the case of the Si-bonded OSiAu2 cluster. However, on the unbonded pristine Au3-O cluster in Figure S7b, the activation barrier for the formation of OCO is only 1.15 kcal/mol. The catalytic ability of the SiAu2 cluster is very low for CO oxidation. The slight difference may be attributed to the size effect of gold clusters [80]. The oxidation of CO in a naked Au 4 cluster occurs through I-IM1 to I-TS1, with a high activation barrier of 37.82 kcal/mol to form OCOO intermediates, as listed in Figure S8a. This high activation barrier was observed in an earlier investigation [56]. From Figure 4a, we note that for the first CO oxidation on SiAu 3 , the activation barrier is only 10.15 kcal/mol from C-IM1 to C-TS1 to form the OOCO intermediate. Moreover, the process is exothermic, with a value of −13.14 kcal/mol. Therefore, the SiAu 3 dimer can significantly contribute to the formation of OOCO intermediates. As shown in Figure 4a, the formed OCOO intermediate is decomposed into CO 2 and OSiAu 3 , with a high activation barrier of 22.59 kcal/mol from C-IM2 to C-TS2. From Figure 4b, we observe that, in the case of Si incorporation into the SiAu 3 -O cluster, the reaction occurs by C-IM5 to C-TS3, with a very low activation barrier of 0.46 kcal/mol for the formation of an OCO intermediate. However, the activation barrier for OCO formation from I-IM3 to I-TS2 is 2.54 kcal/mol in the case of unbonded pristine Au 4 -O in the cluster of Figure S8b. Thus, although the bonded SiAu 3 cluster reduces the activation energy required for CO oxidation compared with the pristine Au 4 , the decomposition of the OCOO intermediate on SiAu 3 still needs to overcome a high activation barrier. The reason for this phenomenon may be due to the different active sites on the Au 4 and SiAu 3 clusters, which affect catalytic ability. kcal/mol).
The oxidation of CO in a naked Au4 cluster occurs through I-IM1 to I-TS1, with a high activation barrier of 37.82 kcal/mol to form OCOO intermediates, as listed in Figure S8a. This high activation barrier was observed in an earlier investigation [56]. From Figure 4a, we note that for the first CO oxidation on SiAu3, the activation barrier is only 10.15 kcal/mol from C-IM1 to C-TS1 to form the OOCO intermediate. Moreover, the process is exothermic, with a value of −13.14 kcal/mol. Therefore, the SiAu3 dimer can significantly contribute to the formation of OOCO intermediates. As shown in Figure 4a, the formed OCOO intermediate is decomposed into CO2 and OSiAu3, with a high activation barrier of 22.59 kcal/mol from C-IM2 to C-TS2. From Figure 4b, we observe that, in the case of Si incorporation into the SiAu3-O cluster, the reaction occurs by C-IM5 to C-TS3, with a very low activation barrier of 0.46 kcal/mol for the formation of an OCO intermediate. However, the activation barrier for OCO formation from I-IM3 to I-TS2 is 2.54 kcal/mol in the case of unbonded pristine Au4-O in the cluster of Figure S8b. Thus, although the bonded SiAu3 cluster reduces the activation energy required for CO oxidation compared with the pristine Au4, the decomposition of the OCOO intermediate on SiAu3 still needs to overcome a high activation barrier. The reason for this phenomenon may be due to the different active sites on the Au4 and SiAu3 clusters, which affect catalytic ability. With regard to CO oxidation on the Au 5 cluster, the CO oxidation on the Au 5 cluster requires an activation energy barrier of 12.45 kcal/mol via J-IM1 to J-TS1 to form the OOCO intermediate, as listed in Figure S9a, which is consistent with the reported values of 13.84 kcal/mol and 18.45 kcal/mol, as calculated by Hyesung et al. in the liter-ature [81]. From Figure 5a, we find that the first CO oxidation process on SiAu 4 passes through D-IM1 to D-TS1, thus overcoming an activation energy barrier of 29.52 kcal/mol to form the OOCO intermediate. In addition, the process is endothermic, with a value of 27.90 kcal/mol. Moreover, as shown in Figure 5a, passing through D-IM2 to D-TS2, the formed OCOO intermediate is decomposed into CO 2 and OSiAu 4 , with an activation barrier of 17.99 kcal/mol; this shows that the catalytic ability of SiAu 4 is much weaker compared with the Au 5 cluster. From Figure 5b, we find that for the oxidation process of the second CO on OSiAu 4 , only a very low 1.15 kcal/mol energy barrier needs to be passed from D-IM4 to D-TS3 for the formation of the OCO intermediate. As for the oxidation process of CO on Au 5 O, an activation energy barrier of 11.30 kcal/mol is required to form the OCO intermediate, which is consistent with the calculation of 10.38 kcal/mol by Liu et al. [68]. Therefore, the second CO oxidation OSiAu 5 is very feasible compared with the OAu 5 cluster. These differences may be due to different active sites and electronic structures [82].
With regard to the Au 6 cluster, as shown in Figure S10a, the oxidation process of CO on the Au 6 cluster requires a very high activation energy barrier of 32.29 kcal/mol from K-IM1 to K-TS1 for the formation of OOCO intermediates. This high activation barrier has been observed in previous investigations by Ramesh et al. [83]. As shown in Figure 6a, an activation energy barrier of 2.31 kcal/mol is required to form the OOCO intermediate from E-IM1 to E-TS1 during the first CO oxidation on SiAu 5 . Thus, the SiAu 5 dimer can significantly contribute to the formation of OCOO intermediates. In addition, the process is exothermic, with a value of −21.68 kcal/mol. From Figure 6a, we note that after E-IM2 to E-TS2, the formed OCOO intermediate is then decomposed into CO 2 and OSiAu 5 , with a relatively low activation energy barrier of 12.92 kcal/mol. The same effect is also shown for the second CO oxidation process. From Figure S10b, we find that the oxidation process of CO on Au 6 O requires a 2.07 kcal/mol activation energy barrier from K-IM5 to K-TS3 for producing the OCO intermediate. However, as shown in Figure 6b, on the OSiAu 5 cluster, only a very low 0.46 kcal/mol activation energy barrier is required to pass through E-IM4 to E-TS3 for the formation of OCO intermediates. The structure is changed before and after binding, and the charge is transferred. Thus, the bound SiAu 5 cluster lowers the activation energy barrier for CO oxidation, and the reaction occurs more readily compared with the Au 6 cluster process. In addition, we also noted that the reactivity and catalytical effects are also affected by supports for different metal oxide surfaces [5,9,20]. Moreover, experimental investigations are important for understanding CO oxidation on SiAu n clusters. We will consider these investigations in the next step of our research.  With regard to CO oxidation on the Au5 cluster, the CO oxidation on the Au5 cluster requires an activation energy barrier of 12.45 kcal/mol via J-IM1 to J-TS1 to form the OOCO intermediate, as listed in Figure S9a, which is consistent with the reported values of 13.84 kcal/mol and 18.45 kcal/mol, as calculated by Hyesung et al. in the literature [81]. From Figure 5a, we find that the first CO oxidation process on SiAu4 passes through D-IM1 to D-TS1, thus overcoming an activation energy barrier of 29.52 kcal/mol to form the OOCO intermediate. In addition, the process is endothermic, with a value of 27.90 kcal/mol. Moreover, as shown in Figure 5a, passing through D-IM2 to D-TS2, the formed OCOO intermediate is decomposed into CO2 and OSiAu4, with an activation barrier of 17.99 kcal/mol; this shows that the catalytic ability of SiAu4 is much weaker compared with the Au5 cluster. From Figure 5b, we find that for the oxidation process of the second CO on OSiAu4, only a very low 1.15 kcal/mol energy barrier needs to be passed from D-IM4 to D-TS3 for the formation of the OCO intermediate. As for the oxidation process of CO on Au5O, an activation energy barrier of 11.30 kcal/mol is required to form the OCO intermediate, which is consistent with the calculation of 10.38 kcal/mol by Liu et al. [68]. Therefore, the second CO oxidation OSiAu5 is very feasible compared with the OAu5 cluster. These differences may be due to different active sites and electronic structures [82]. With regard to the Au6 cluster, as shown in Figure S10a, the oxidation process of CO on the Au6 cluster requires a very high activation energy barrier of 32.29 kcal/mol from K-IM1 to K-TS1 for the formation of OOCO intermediates. This high activation barrier has been observed in previous investigations by Ramesh et al. [83]. As shown in Figure 6a, an activation energy barrier of 2.31 kcal/mol is required to form the OOCO intermediate from E-IM1 to E-TS1 during the first CO oxidation on SiAu5. Thus, the SiAu5 dimer can significantly contribute to the formation of OCOO intermediates. In addition, the process is exothermic, with a value of −21.68 kcal/mol. From Figure 6a, we note that after E-IM2 to E-TS2, the formed OCOO intermediate is then decomposed into CO2 and OSiAu5, with a relatively low activation energy barrier of 12.92 kcal/mol. The same effect is also shown for the second CO oxidation process. From Figure S10b, we find that the oxidation process of CO on Au6O requires a 2.07 kcal/mol activation energy barrier from K-IM5 to K-TS3 for producing the OCO intermediate. However, as shown in Figure 6b, on the OSiAu5 cluster, only a very low 0.46 kcal/mol activation energy barrier is required to pass through E-IM4 to E-TS3 for the formation of OCO intermediates. The structure is changed before and after binding, and the charge is transferred. Thus, the bound SiAu5 cluster lowers the activation energy barrier for CO oxidation, and the reaction occurs more readily compared with the Au6 cluster process. In addition, we also noted that the reactivity and catalytical effects are also affected by supports for different metal oxide surfaces [5,9,20]. Moreover, experimental investigations are important for understanding CO oxidation on SiAun clusters. We will consider these investigations in the next step of our research.

Computational Methods
To determine the most stable structures for the SiAun (n = 1-5) cluster, we artificial bee colony (ABC) algorithm to carry out a global search by using the A program [84,85]. Initially, we used the ABCluster program to generate 100 clus tures for SiAun (n = 1-5) by the B3LYP functional [86]. The aug-cc-pVDZ basis [8 was selected for Si atoms. Pseudopotential ECP60MDF and aug-cc-pVDZ-PP ba sets were used for Au atoms. After completing the structure search, we picke lowest-energy structures and reoptimized them again by using the CAM-B3L tional [91], a long-range-corrected hybrid GGA functional.
We used the CAM-B3LYP functional to perform geometry optimizations quency calculations of the stationary points for CO oxidation on the SiAun clu aug-cc-pVDZ basis set was selected for C, Si, and O atoms. Pseudopotential EC and aug-cc-pVDZ-PP basis sets were used for Au atoms. The calculated result

Computational Methods
To determine the most stable structures for the SiAu n (n = 1-5) cluster, we used the artificial bee colony (ABC) algorithm to carry out a global search by using the ABCluster program [84,85]. Initially, we used the ABCluster program to generate 100 cluster structures for SiAu n (n = 1-5) by the B3LYP functional [86]. The aug-cc-pVDZ basis [87][88][89][90][91] set was selected for Si atoms. Pseudopotential ECP60MDF and aug-cc-pVDZ-PP basis [89,90] sets were used for Au atoms. After completing the structure search, we picked out the lowestenergy structures and reoptimized them again by using the CAM-B3LYP functional [91], a long-range-corrected hybrid GGA functional.
We used the CAM-B3LYP functional to perform geometry optimizations and frequency calculations of the stationary points for CO oxidation on the SiAu n cluster. The aug-cc-pVDZ basis set was selected for C, Si, and O atoms. Pseudopotential ECP60MDF and aug-cc-pVDZ-PP basis sets were used for Au atoms. The calculated results indicate that none of the stationary points have imaginary frequencies, except for the transition state, which has only one imaginary frequency. Intrinsic reaction coordinate calculations [92][93][94][95] were performed by using the HPC algorithm to determine the transition states connected with the corresponding reactants and products. In addition, the stability of the DFT wave functions of all species was tested by using the Gaussian 16 keyword (stable = opt) [96,97]. All of the DFT calculations were performed by using the Gaussian 16 software package [98].

Conclusions
In conclusion, the calculated results show the effects of CO oxidation on the reaction activity and catalytic activity of silicon-bound gold clusters. The results show that compared with the original small Au n (n = 1-3) cluster, the clusters incorporating silicon SiAu n (n = 1-2) have higher catalytic activity for the first CO oxidation reaction and a lower activation barrier, while the catalytic effects of the second CO oxidation reaction did not improve. For the SiAu n (n = 3 or 5) cluster, we found that compared with the Au n (n = 4 or 6) cluster, the activation energy barriers were reduced for both the first CO oxidation reaction and the second CO oxidation reaction. In addition, we found that the catalytic performance of incorporating silicon atoms on an odd Au cluster is better than that of an even Au cluster. To sum up, our results emphasize the importance of incorporating heterogeneous impurities in the design of gold clusters with catalytic activity.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/molecules28041917/s1, Figure S1. Geometrical optimizations of the lowest-energy structures of Au n (n = 1-6) based on theory at the CAM-B3LYP/aug-cc-pVDZ-PP level. Figure S2. Geometrical optimizations of the lowest-energy structures of Au n Si (n = 1-5) based on theory at the CAM-B3LYP/aug-cc-pVDZ-PP level. Figure S3. Optimized lowest-energy geometries of CO adsorbed with Au n (n = 1-6) and the corresponding adsorption energies at the CAM-B3LYP/aug-cc-pVDZ-PP level (in kcal/mol). Figure S4. CO adsorption on Au atoms of Au n (n = 1-2) cluster structures and the corresponding adsorption energies at the CAM-B3LYP/aug-cc-pVDZ-PP level (in kcal/mol). Figure S5. Potential energy profile of CO oxidation on Au atoms at the CAM-B3LYP/aug-cc-pVDZ-PP level. (a) Oxidation of CO on the Au cluster and (b) oxidation of CO on the OAu cluster (in kcal/mol). Figure S6. Potential energy profile of CO oxidation on Au 2 atoms at the CAM-B3LYP/aug-cc-pVDZ-PP level. (a) Oxidation of CO on the Au 2 cluster and (b) oxidation of CO on the OAu 2 cluster (in kcal/mol). Figure S7. Potential energy profile of CO oxidation on Au 3 atoms at the CAM-B3LYP/aug-cc-pVDZ-PP level. (a) Oxidation of CO on the Au 3 cluster and (b) oxidation of CO on the OAu 3 cluster (in kcal/mol). Figure S8. Potential energy profile of CO oxidation on Au 4 atoms at the CAM-B3LYP/aug-cc-pVDZ-PP level. (a) Oxidation of CO on the Au 4 cluster and (b) oxidation of CO on the OAu 4 cluster (in kcal/mol). Figure S9. Potential energy profile of CO oxidation on Au 5 atoms at the CAM-B3LYP/aug-cc-pVDZ-PP level. (a) Oxidation of CO on the Au 5 cluster and (b) oxidation of CO on the OAu 5 cluster (in kcal/mol). Figure S10. Potential energy profile of CO oxidation on Au 6 atoms at the CAM-B3LYP/aug-cc-pVDZ-PP level. (a) Oxidation of CO on the Au 6 cluster and (b) oxidation of CO on the OAu 6 cluster (in kcal/mol). Figure S11. The structure and energy of various substances in the oxidation pathway for CO on AuSi (in kcal/mol). Figure S12. The structure and energy of various substances in the oxidation pathway for CO on Au 2 Si (in kcal/mol). Figure S13. The structure and energy of various substances in the oxidation pathway for CO on Au 3 Si (in kcal/mol). Figure S14. The structure and energy of various substances in the oxidation pathway for CO on Au 4 Si (in kcal/mol). Figure S15. The structure and energy of various substances in the oxidation pathway for CO on Au 5 Si (in kcal/mol).